A walk reel mower includes a pair of inclined rigid links for mounting the reel cutting unit to the reel mower frame for rolling about a longitudinal axis, and a pair of vertical support arms for mounting the reel cutting unit to the reel mower frame for pitching about a transverse axis. An integrated gearbox houses both the traction and reel drives, including the differential that is part of the traction drive, as well as a parking brake. A flexible drive shaft powers the cutting reel from the gearbox and is made from materials that do not require petroleum based lubricants to avoid the possibility of damage to the turf or grass. A single control handle located on the handle of the mower actuates both the reel and traction drives. The reel cutting unit includes a back plate which has a portion formed as a hollow beam for strength. The reel cutting unit also has a pivot axis for the bedknife allowing adjustment of the bedknife relative to the cutting reel without changing the longitudinal location of the front edge of the bedknife to ensure consistent cutting of the cutting unit. Finally, an improved mounting for the grass basket used on the cutting unit is disclosed which mounting avoids inadvertent disengagement of the grass basket from the cutting unit.